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Spectrogram
.]] A spectrogram is a time-varying spectral representationS. Haykin, editor, Advances in Spectrum Analysis and Array Processing, vol.1, Prentice-Hall, 1991. (forming an image) that shows how the spectral density of a signal varies with time. In the field of time–frequency signal processing, it is one of the most popular quadratic Time-Frequency Distribution that represents a signal in a joint time-frequency domain B. Boashash, editor, “Time-Frequency Signal Analysis and Processing – A Comprehensive Reference”, Elsevier Science, Oxford, 2003; ISBN 0080443354 and that has the property of being positive. Also known as spectral waterfalls, sonograms, voiceprints, or voicegrams, spectrograms are used to identify phonetic sounds, to analyse the cries of animals; they were also used in many other fields including music, sonar/radar, speech processingJL Flanagan, Speech Analysis, Synthesis and Perception, Springer- Verlag, New York, 1972, seismology, etc. The instrument that generates a spectrogram is called a spectrograph and is equivalent to a sonograph. Format The most common format is a graph with two geometric dimensions: the horizontal axis represents time, the vertical axis is frequency; a third dimension indicating the amplitude of a particular frequency at a particular time is represented by the intensity or colour of each point in the image. There are many variations of format: sometimes the vertical and horizontal axes are switched, so time runs up and down; sometimes the amplitude is represented as the height of a 3D surface instead of color or intensity. The frequency and amplitude axes can be either linear or logarithmic, depending on what the graph is being used for. Audio would usually be represented with a logarithmic amplitude axis (probably in decibels, or dB), and frequency would be linear to emphasize harmonic relationships, or logarithmic to emphasize musical, tonal relationships. Generation signal. In this case the signal frequency is modulated with a sinusoidal frequency vs. time profile]] Spectrograms are usually created in one of two ways: approximated as a filterbank that results from a series of bandpass filters (this was the only way before the advent of modern digital signal processing), or calculated from the time signal using the short-time Fourier transform (STFT). These two methods actually form two different quadratic Time-Frequency Distributions, but are equivalent under some conditions. The bandpass filters method usually uses analog processing to divide the input signal into frequency bands; the magnitude of each filter's output controls a transducer that records the spectrogram as an image on paper.Illustration of an electro-mechanical spectrograph Creating a spectrogram using the STFT is usually a digital process. Digitally sampled data, in the time domain, is broken up into chunks, which usually overlap, and Fourier transformed to calculate the magnitude of the frequency spectrum for each chunk. Each chunk then corresponds to a vertical line in the image; a measurement of magnitude versus frequency for a specific moment in time. The spectrums or time plots are then "laid side by side" to form the image or a three-dimensional surface.Spectrogram definition The spectrogram of a signal s(t) can be estimated by computing the squared magnitude of the STFT of the signal s(t), as shown below: : \mathrm{spectrogram}(t,\omega)=\left|\mathrm{STFT}(t,\omega)\right|^2STFT spectrogram details Applications in music by Aphex Twin]] * Early analog spectrograms were applied to a wide range of areas including the study of bird calls, with current research continuing using modern digital equipmentBird Songs and Spectrograms of Southern Tuscany and applied to all animal sounds. Contemporary use of the digital spectrogram is especially useful for studying frequency modulation (FM) in animal calls. Specifically, the distinguishing characteristics of FM chirps, broadband clicks, and social harmonizing are most easily visualized with the spectrogram. A particularly interesting example for the use of the spectrogram is in analysis of the vocalizations of a pod of Dolphins. * Spectrograms are useful in assisting in overcoming speech defects and in speech training for the portion of the population that is profoundly deafA wearable tactile sensory aid for profoundly deaf children * The studies of phonetics and speech synthesis are often facilitated through the use of spectrogramsSpectrogram ReadingPraat - doing phonetics by computer. * By reversing the process of producing a spectrogram, it is possible to create a signal whose spectrogram is an arbitrary image. This technique can be used to hide a picture in a piece of audio and has been employed by several electronic music artistsSeveral sound spectrogram examples, including the one by Aphex Twin. See also steganography. * Some modern music is created using spectrograms as an intermediate medium; changing the intensity of different frequencies over time, or even creating new ones, by drawing them and then inverse transforming. See Audio timescale-pitch modification and Phase vocoder. * Spectrograms can be used to analyze the results of passing a test signal through a signal processor such as a filter in order to check its performanceExample of using spectrograms to check filter responses. * High definition spectrograms are used in the development of RF and microwave systems High definition spectrograms of common RF signals * Spectrograms are now used to display S-parameters measured with vector network analyzers Spectrograms for vector network analyzers * The US Geological Survey now provides real-time spectrogram displays from seismic stations Real-time spectrogram displays from seismic stations Limitations and resynthesis From the formula above, it appears that a spectrogram contains no information about the exact phase of the signal that it represents. For this reason, it is not possible to reverse the process and generate a copy of the original signal from a spectrogram, though in situations where the exact initial phase is unimportant (of which audio may be one), it may be possible to generate a useful approximation of the original signal. The Analysis & Resynthesis Sound Spectrographhttp://arss.sourceforge.net is an example of a computer program that attempts to do this. In fact, there is some phase information in the spectrogram, but it appears in another form, as time delay (or group delay) which is the dual of the Instantaneous Frequency; an experiment explaining and relating these two concepts is described in B. Boashash, "Estimating and Interpreting the Instantaneous Frequency of a Signal-Part I: Fundamentals", Proceedings of the IEEE, Vol. 80, No. 4, pp. 519-538, April 1992, doi:10.1109/5.135376 See also * Short-time Fourier transform * Spectrometer * Spectrum * Wavelet transform * Reassignment method * Time-frequency representation * Strobe tuners * Scaleogram * The Bloop References External links * Further information on creating a signal whose spectrogram is an arbitrary image Category:Acoustics Category:Signal processing Category:Time–frequency analysis ar:صورة طيفية ca:Espectrograma de:Spektrogramm es:Espectrograma eo:Spektrogramo fr:Spectrogramme it:Spettrogramma ko:스펙트로그램 nl:Spectrogram ja:スペクトログラム pl:Spektrogram pt:Espectrograma ru:Спектрограмма sv:Spektrografi